⁑Author to whom correspondance should be addressed: Tel +45 93 90 39 70; [email protected]
© 2018. Published by The Company of Biologists Ltd.
Turbulent flow reduces oxygen consumption in the labriform swimming shiner
perch, Cymatogaster aggregata
J. M. van der Hoop1⁑, M. L. Byron2,3, K. Ozolina4, D. L. Miller5, J. L. Johansen6, P.
Domenici7 and J. F. Steffensen8
1 Zoophysiology, Department of Bioscience, Aarhus University, 8000 Aarhus C, Denmark
2 Department of Ecology and Evolutionary Biology, University of California Irvine,
Irvine CA 92697 3 Current address: Department of Mechanical and Nuclear Engineering, The
Pennsylvania State University, University Park, PA, 16802, USA 4 Faculty of Biology, Medicine and Health, The University of Manchester, Manchester
M13 9NT, United Kingdom 5 Centre for Research into Ecological & Environmental Modelling and School of
Mathematics & Statistics, University of St Andrews, Fife, Scotland 6 New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates
7 CNR – IAMC, Istituto per l’Ambiente Marino Costiero, Località Sa Mardini, 09072
Torregrande, Oristano, Italy 8 Department of Biology, University of Copenhagen, DK-3000 Helsingør, Denmark
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http://jeb.biologists.org/lookup/doi/10.1242/jeb.168773Access the most recent version at First posted online on 3 April 2018 as 10.1242/jeb.168773
Abstract
Fish swimming energetics are often measured in laboratory environments which attempt
to minimize turbulence, though turbulent flows are common in the natural environment.
To test whether the swimming energetics and kinematics of shiner perch Cymatogaster
aggregata (a labriform swimmer) were affected by turbulence, two flow conditions were
constructed in a swim-tunnel respirometer. A low-turbulence flow was created using a
common swim-tunnel respirometry setup with a flow straightener and fine-mesh grid to
minimize velocity fluctuations. A high-turbulence flow condition was created by
allowing large velocity fluctuations to persist without a flow straightener or fine grid. The
two conditions were tested with Particle Image Velocimetry to confirm significantly
different turbulence properties throughout a range of mean flow speeds. Oxygen
consumption rates of the swimming fish increased with swimming speeds and pectoral
fin beat frequencies in both flow conditions. Higher turbulence also caused a greater
positional variability in swimming individuals (vs. low-turbulence flow) at medium and
high speeds. Surprisingly, fish used less oxygen in high turbulence compared to low-
turbulence flow at medium and high swimming speeds. Simultaneous measurements of
swimming kinematics indicated that these reductions in oxygen consumption could not
be explained by specific known flow-adaptive behaviours such as Kármán-gaiting or
entraining. Therefore, fish in high-turbulence flow may take advantage of the high
variability in turbulent energy through time. These results suggest that swimming
behavior and energetics measured in the lab in straightened flow, typical of standard
swimming respirometers, might differ from that of more turbulent, semi-natural flow
conditions.
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Keywords: vortex, eddy, gait, swimming kinematics, metabolism, space use
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Introduction
The complex habitats in which many marine organisms live are governed by
stochastic, multiscale processes. However, unpredictability is often purposefully limited
in studies of fish-flow interaction. Water tunnels, flumes and other apparatuses are
usually fitted with honey combs or grids that straighten flow streamlines and minimize
turbulent velocity fluctuation (Bainbridge, 1958; Bell and Terhune, 1970; Webb, 1975;
Steffensen et al., 1984; Hove et al., 2000; Drucker and Lauder, 2002).
In the interest of mimicking the natural environment, recent laboratory
experiments have sought to explore the relationship between fish and more complex
flows (as reviewed in Liao 2007). Flows have been altered via the introduction of
boulders (Shuler et al., 1994) and logs (McMahon and Gordon, 1989); plexiglass
structures (Fausch, 1993); cones, spheres, and half-spheres (Sutterlin and Waddy, 1975);
horizontally- or vertically-oriented circular cylinders (Sutterlin and Waddy, 1975; Webb,
1998; Montgomery et al., 2003; Cook and Coughlin, 2010; Tritico and Cotel, 2010); and
D-section cylinders (Liao, 2003; Liao, 2004; Liao, 2006; Taguchi and Liao, 2011). Other
researchers have introduced fluctuations in water flow speed (Enders et al., 2003; Roche
et al., 2014) or body-scale streamwise vortices (Maia et al., 2015). All these methods
have served to introduce regular hydrodynamic perturbations in otherwise straightened
flows, providing a more realistic approximation of the natural habitat of the animals
studied. In some specific cases, the consistent flow features produced by these
perturbations are exploited by fish to reduce the metabolic cost of swimming (Enders et
al., 2003; Liao, 2004).
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Fish response to these “altered” or complex flows (i.e., non-turbulent but vortex-
perturbed) can be highly variable (see e.g. Cotel and Webb, 2012). It has been
hypothesized that swimming in unsteady flows increases energy consumption by
requiring additional swimming manoeuvres (Blake, 1979; Weatherley et al., 1982;
Puckett and Dill, 1984; Webb, 1991; Boisclair and Tang, 1993; Maia et al., 2015). While
some studies have shown that fluctuating flows reduce maximum swimming speed
(Pavlov et al., 2000; Tritico and Cotel, 2010; Roche et al., 2014) and increase energy
expenditure (Enders et al., 2003; Maia et al., 2015), other studies have found no effect of
flow variability on performance metrics in a variety of species (Ogilvy and DuBois,
1981; Nikora et al., 2003). The effects of complex flows on fish swimming performance
and oxygen consumption rates are dependent on the magnitude of the turbulence/velocity
fluctuations (Pavlov et al., 2000; Lupandin, 2005; Tritico and Cotel, 2010; Webb and
Cotel, 2010; Roche et al., 2014) and likely tied to the fish’s swimming behaviour (body-
caudal-fin, BCF vs. median-paired-fin, MPF). Swimming performance may also be
improved if fish can sense and respond to periodic vortex structures (Liao, 2007).
However, these controlled situations may not be directly comparable to many natural
habitats in which fish live, where aperiodic components of the flow can be dominant.
It is important to note that many of these “altered” flows do not fit the classical
definition of turbulence; they include strong periodic components and little stochasticity,
which is a key feature of turbulence (Tennekes and Lumley, 1972; Pope, 2000). In the
biological literature, turbulence is described as “highly irregular” (Vogel, 1994) and
“chaotic” (Denny, 1993). Therefore, turbulence should be distinguished from highly
periodic coherent structures such as waves or vortex streets. These structures may be
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influenced by turbulence or have turbulence superimposed upon them, but are not
themselves “turbulence”.
How fish respond to unstraightened, irregular flows in a swimming respirometer,
as compared to the straightened and fluctuation-minimizing flows often used in
laboratory experiments, is largely unknown. In most previous studies involving “altered”
flows (above), periodic fluctuations were introduced by adding features to otherwise
straightened flows. In the present study, an unstraightened flow was compared to a
standard, straightened flow. In both flows, energy was introduced by an impeller, and the
resulting turbulence was allowed to decay over the length of the respirometer. In the
unstraightened (high-turbulence) condition, flow was unimpeded from the impeller to the
working section, save for a large-opening grid that served to confine the animal to the
working section of the swim tunnel (the section to which the fish is confined when
swimming; Ellerby and Herskin, 2013). Animals in the working section therefore
encountered a field of aperiodic vortices and eddies which remained large relative to the
size of the chamber. In the straightened (low-turbulence) condition, the flow features
were quantifiably reduced in size via the inclusion of a honeycomb flow straightener and
subsequent fine-mesh grid. The flow straightener includes tubes with a sufficiently small
diameter to damp out velocity fluctuations and eliminate large eddies before they are
advected into the test section (Seo, 2013). In the unstraightened flow, turbulence
intensity, turbulent kinetic energy, dissipation rate, and other metrics were substantially
increased relative to the straightened flow. These two configurations produced two
distinct conditions: high-turbulence flow (HTF) and low-turbulence flow (LTF).
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The metabolic cost of swimming in these two flows was examined, and the
swimming kinematics were compared between the two conditions. Although previous
studies have shown variable effects of turbulence on the metabolic cost of swimming
(e.g. cited above), it was expected that oxygen consumption rates would be greater in
HTF compared to LTF, because additional postural control and unsteady motion would
likely be necessary to respond to aperiodic fluctuations in the flow field.
Materials and Methods
Particle Image Velocimetry (PIV)
Setup and Imaging Technique
Particle Image Velocimetry (PIV) was used to investigate and quantify turbulence
in the swim-tunnel respirometer (Figure 1). The vertical midplane of the working area
was illuminated by a 1 W laser of wavelength 445 nm, spread into a thin sheet via a
rigidly-attached cylindrical lens (S3 Spyder III Arctic, Wicked Lasers; Figure 1). At
speeds >0.30 m s-1, images of the vertical midplane were collected at 872 Hz with an
exposure time of 1146 μs, using a high-speed, high-resolution camera (HHC Mega Speed
PRO X4; Mega Speed, San Jose, U.S.A.). At speeds < 0.30 m s-1, images were collected
at 500 Hz with an exposure time of 2000 μs. Image resolution was 1280 × 720 pixels at
higher speeds and 1280 × 1024 pixels for lower speeds. Jo
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The flow was seeded with hydrated Artemia cysts (Sanders’ Premium Great Salt
Lake Artemia Cysts) at an approximate seeding density of 16 cm-2 throughout the
illuminated midplane. To ensure neutral buoyancy of the tracer particles, dry Artemia
cysts were mixed into beakers of seawater at approximately 40 g L-1, and left undisturbed
for a minimum of 40 min to allow positively or negatively buoyant particles to rise or fall
out of suspension (Lauder and Clark, 1984). Positively buoyant particles were skimmed
from the water surface, and suspension containing near-neutrally buoyant particles was
removed and added to the swim-tunnel respirometer. Artemia cysts from the Great Salt
Lake strain are known to have a mean diameter of approximately 250 μm (Vetriselvan
and Munuswamy, 2011), which in the camera view corresponds to approximately 1 pixel.
Light scattering from these tracers increased the average diameter seen in the camera
view to 2-3 pixels, as is appropriate for PIV (Melling, 1997; Raffel et al., 2007).
Image Analysis
Images were batch processed in Adobe Photoshop to adjust balance and enhance
contrast before performing vector computation via two-pass iteration in DaVis (LaVision
GmbH, Goettingen, Germany). Subwindows were 64 × 64 pixels (13.4 × 13.4 mm) and
32 × 32 pixels (6.7 × 6.7 mm) with 50% overlap, resulting in flow resolved to 3.3 mm.
This is sufficient to examine the scales of interest, since flow structures smaller than 3.3
mm are not likely to affect fishes of the size used in this experiment (Tritico and Cotel,
2010). Vectors were computed for the entire working area in both HTF and LTF.
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Flow Characterization
Several of the many parameters available to describe the level of variability in
turbulent flows (Cotel and Webb, 2012) were calculated for both HTF and LTF. These
parameters are defined and described in detail in Appendix SI (Supporting Information).
They are , the turbulent velocity scale; , the turbulent kinetic energy; , the
turbulence intensity; , the enstrophy (the square of vorticity); , the energy dissipation
rate; and , the integral lengthscales in x and z; , the Taylor microscale; and , the
Kolmogorov microscale. All parameters (with the exception of the integral lengthscales
and spectra) were calculated as spatiotemporally-varying quantities, defined at each x-z
point for each frame (where a frame is one PIV image-pair). Quantities were averaged in
time to calculate mean quantities, with 95% confidence intervals calculated via
bootstrapping in time (approximately 6 s per flow speed and turbulence condition, with 8
data points calculated throughout the range of tested speeds). The outer 2 cm of each
frame (close to the grid and walls) were not included in the averages to avoid including
the effects of boundary layers. Integral lengthscales were found by calculating the
appropriate autocorrelations in x and z.
Flow Properties
Non-overlapping 95% CIs indicated that HTF had significantly higher average
values of , , , and compared to LTF (Figure S1), across the range of tested
flow speeds. The difference between HTF and LTF generally increased with flow speed:
, , and all increased with flow speed in HTF, but in LTF, these parameters
remained low and relatively constant despite the increasing flow speed. was higher in
HTF than in LTF but was highest at low speeds and reaches a plateau as speed increases
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(0-0.4 m s-1; Figure S1D). This was expected, as represents the ratio of fluctuations to
mean flow; as mean flow increases, fluctuations will become stronger and will remain
constant.
At high speeds, was approximately 150% higher in HTF than in LTF. At the
highest tested speed, was 500% higher in HTF; was 170% higher; and was
370% higher. For the difference in turbulence properties across the full range of flow
speeds tested, see supplemental figures. The turbulence properties observed in the
laboratory-generated flow (in both HTF and LTF) were comparable to those that would
be experienced by C. aggregata in its natural habitat of coastal estuaries, bays, and
streams (see Table 1).
Three turbulent lengthscales were calculated to illustrate the differences in eddy
sizes between HTF and LTF. The Taylor microscale (representing the average distance
between stagnation points within the flow) and streamwise integral lengthscale
(representing the overall average eddy size) were both larger in HTF than in LTF, and the
Kolmogorov scale was generally smaller in HTF (Figure S2)1. The relative sizes of
these three scales signify that in HTF, fish were swimming through a larger range of
spatial scales within the flow. Additionally, the vorticity field suggests differences in
overall flow structure between the two flow conditions (Figure 2). To verify that the flow
did not contain any significant periodic components, the frequency spectra of both HTF
and LTF were calculated throughout the tested velocity range (Figure S3). No discrete
1 We note that the Kolmogorov scale in our experiments, averaging approximately 0.2-0.4mm, is aligned
with the expected values for small-scale ocean turbulence (0.3 – 2mm; Jiménez 1997). However, it is not
possible to match the larger lengthscales to the animal’s natural habitat. In an experimental context, these
larger lengthscales are bounded by the respirometer’s overall size and therefore cannot approach the wind-
and tide-driven scales typical of the coastal ocean.
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periodicity, such as that produced by vortex shedding or driven by the flow impeller, was
observed within the working section, and the spectra were consistent with classic
turbulent spectra showing an energetic cascade from low to high frequencies. As
expected, HTF contained more energy overall across all frequencies (Figure S3).
To summarize, two different flow conditions were created in a swimming
respirometer. Both of these flows were turbulent, containing aperiodic velocity
fluctuations. Neither flow contains large, periodic coherent structures (such as the von
Kármán vortex street typically shed from a bluff body; Figure S3). However, HTF is
measurably more turbulent than LTF: it has larger velocity fluctuations at a given speed
(higher turbulence intensity; TI), is dissipating energy at a higher rate ( ) and contains a
larger variance of eddy sizes (Lxx, Lzz, , ) as well as stronger extremes of vorticity ( ;
Figures S1 and S2). Therefore, a significant difference was expected in the energetics of
fish swimming in these two flow conditions.
Fish Collection and Husbandry
Shiner perch, Cymatogaster aggregata (Gibbons, 1854) were collected by beach
seine at Jackson Beach, San Juan Island, Washington, U.S.A. (48°31’ N, 123°01’ W) in
July and August 2013. Fish body length (BL, mean±SD) measured 12.1±0.3 cm, and
weight was 40±7.1 g. Fish were kept in 120 × 56 × 15 cm and 90 × 59 × 30 cm tanks at
the University of Washington’s Friday Harbor Laboratories. Fish were kept in
recirculating sea water, where they fed on plankton present in the water. Fish were fasted
for a minimum of 4 hours prior to experimental trials. Ambient seawater temperature
followed ocean conditions of the area and ranged from 12 - 14°C. After capture,
individuals were maintained in aquaria for at least 3 days before their first experimental
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trial, and were given a minimum of two days to recover between trials. Eight fish
performed trials in both the low- and high-turbulence conditions were used for analysis.
The order of low and high turbulence exposure was randomized for each individual by
flipping a coin.
Swimming Energetics
Experiments were conducted in an 8.31 L clear Steffensen Model 1 Plexiglas
swimming respirometer ([email protected]) with a working section of 9.0 × 26.0 ×
11.0 cm (width × length × depth). LTF and HTF were induced by inserting two different
grid conditions (Figure 1). For LTF, the tunnel was fitted with a 9.4 × 10.6 × 3.3 cm
(width × depth × thickness) honeycomb straightener (0.6 cm tube diameter) followed by
a 0.01 cm2 square mesh mounted on a 9.2 × 11.9 × 1.7 cm (w × d × t) plastic grid (1.2 ×
1.2 cm opening size). This fine mesh reduced the size of the incoming coherent flow
structures, further straightening the flow. For HTF, the tunnel was fitted with a 9.2 × 11.8
cm (w × d) large-opening grid (opening size 2.45 × 2.65 cm (l × h), coated wire thickness
2.7 mm on average). These large openings constrained the fish to the desired test section
while still allowing relatively large eddies (approximately 60% of fish body depth) to
enter the test section. The honeycomb straightener was not present in the HTF regime.
Flow speed within the working section was driven by an impeller attached to an
AC motor and motor control (DRS71S4/FI and Movitrac LTE-B B0004 101-1-20,
respectively; SEW Eurodrive, Wellford, SC), and was calibrated prior to experiments
with a Hontzsch TAD W30 flow-meter (Hontzsch, Waiblingen, Germany). Flow speed is
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hereafter reported in body lengths per second, BL s-1. Water temperature during trials was
maintained between 12.9 – 13.0°C by an external chiller.
Before each trial, fish were acclimated in the test section for a minimum of 4:00
h:m (max 8:53 h:m), swimming at 0.5 BL s-1. After acclimation, speed was increased by
0.5 BL s-1 every 30 minutes up to a maximum of 4.5 BL s-1 (the max speed reached by
any fish; max 9 speed measurements total for a given fish). Solid blocking effects were
accounted for based on criteria established by Bell and Terhune (1970). Each fish
performed LTF and HTF trials in a randomized order; the time of day of the two trials
was held constant for a given fish to eliminate potential effects of photoperiod on fish
metabolism and allow direct comparison between HTF and LTF for the same individual.
The rate of oxygen consumption (ṀO2; mg O2 kg-1 h-1) was obtained through intermittent
flow respirometry (Steffensen, 1989). Oxygen was measured with a Presens Fibox 3 fibre
optic oxygen meter (Presens, Germany) inserted into the flushing chimney, and ṀO2 was
calculated in LoliRESP as described in (Steffensen, 1989). Three oxygen determinations
were made at each swimming speed, with 180 s flush, 120 s wait, and 600 s measurement
periods comprising a 15-minute cycle (Svendsen et al., 2016). Following each trial,
oxygen consumption was measured in the closed, empty respirometer to measure
background bacterial respiration rates. The measured bacterial respiration was then
subtracted from all ṀO2 measurements in that trial. Bacterial respiration was not
measured for two trials (Fish 5 LTF, Fish 13 HTF); the average bacterial respiration from
all other trails was subtracted from total measured ṀO2.
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Kinematics and space use
All swimming kinematics, including both fin beat frequencies and fish position
within the working section, were filmed at 30 fps with a tripod-mounted Casio Exilim
EX-FH100 camera filming horizontally. A mirror was placed above the respirometer’s
working section at 45° to provide simultaneous lateral and aerial views of the swimming
fish, similar to the schematic shown in Figure 1. Kinematics were measured at three
distinct swimming speeds: low (0.5 BL s-1), medium (1.5 BL s-1) and high (shared Umax;
range 3.5-4.5 BL s-1, mean 3.9 BL s-1) swimming speeds. High swimming speed is
defined as the shared Umax, being the highest flow velocity attained by a given individual
before fatigue in both low- and high-turbulence trials (e.g., if a fish attained 3.5 BL s-1 in
LTF and 4.0 BL s-1 in HTF, the shared Umax is 3.5 BL s-1). Fatigue was defined as when a
fish could no longer swim unassisted and rested against the back grid for >5 s; a speed
level was “attained” if a fish performed all flushing cycles at that flow speed. These three
levels were chosen to illustrate swimming kinematics throughout a range of speeds and to
simplify analyses relative to the more highly-resolved analysis.
Spatial Position
The three-dimensional position coordinates of the tip of the
snout of each fish were digitized in Tracker v. 4.81 (Brown, 2014). Coordinates were
digitized every 10 frames (equivalent to 3 fps) for the last 180 s of the second (of three)
600 s measurement periods. For each trial, the centroid and standard
deviation of the 3D snout coordinate were calculated for each trial, with the
standard deviation reflecting some measure of variance overall (see e.g. Figure 3).
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Pectoral Fin and Tail Beat Frequency
Pectoral and caudal fin use were determined from video footage at the
previously-defined low, medium and high flow velocities. The time of adduction
of the pectoral fin and of complete cycles of left and right displacement of the
caudal fin were recorded (see e.g., Drucker and Jensen, 1996). We calculated the
pectoral and caudal fin beat frequencies (Hz) as the reciprocal of the mean waiting
time between beats (1./mean(diff(beat time))) over the 180 s measurement period
(Figure S4). The gait transition speed (Upc) in C. aggregata (12 cm) has been
reported ~3.5 BL s-1 (e.g., Mussi et al., 2002) and we observed some use of the
caudal fin, in line with previous work. However, a transition to exclusively caudal
fin locomotion was not observed in any fish.
Statistical Analyses
Swimming energetics
Non-linear mixed effects models fitted by restricted maximum likelihood (using
nlme in nlme; Pinheiro et al., 2017) were used to compare the relationship of oxygen
consumption (MO2; mg O2 kg-1 h-1) and speed (U; BL s-1) between individual fish under
different turbulence conditions (See Appendix SIV; R version 3.4.1; R Core Team,
2017). Following (Roche et al., 2014), we fitted a model of the functional form:
MO2 = a +bUc (1)
For each of a, b, c, two parameters were estimated: one for each condition (for a
total of 6 fixed effects parameters). A random effect was used to account for per-fish
variation. Visual inspection of residuals against fish and speed revealed no issue with
heteroscedasticity. Plots of observed vs. fitted values showed good agreement between
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the data and model (Appendix SIV; Zuur et al., 2010). A post-hoc paired t-test was used
to detect differences in oxygen consumption between conditions at each speed, with a
False Discovery Rate correction for multiple comparisons (Benjamini and Hochberg,
1995).
Kinematics and Space Use
To assess how MO2 changed with fin beat frequency, we fitted a generalized
additive model (Wood, 2017) to the MO2, using pectoral or caudal fin beat (Hz) as
separate explanatory variables. We used factor-smooth interactions (Baayen et al., 2016)
to fit two levels of a smoothed function of measured beat frequency, one for each flow
condition. Such terms fit the base level of the factor as a smooth, then model deviations
from that smooth for the other level, thus information is shared between the models while
allowing for a flexible relationship that makes no assumptions about functional form.
Fish ID was included as a random effect. Models were fitted by restricted maximum
likelihood.
Fit for the generalized additive model of oxygen consumption as a function of
pectoral fin beat frequency was assessed using standard plots (Wood, 2017). The factor-
smooth interaction was sufficiently flexible to model the shape of the relationship (6.489
effective degrees of freedom, given a maximum basis complexity of 20), deviance
residuals appeared to be approximated normal, showed little pattern with increasing
values of the linear predictor (hence did not have an issue with heteroscedasticity) and the
relationship between fitted and observed values of oxygen consumption was
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approximately linear. The random effect for fish ID approximated normal from a Q-Q
plot.
We attempted to fit a similar model to the relationship between oxygen
consumption and caudal fin beat frequency, however the model fit was unsatisfactory as
64.6% of the time the fin beat frequency was recorded as zero, limiting model fitting
options. Given the poor fit of our model we do not present any modelling results for
caudal fin beat frequency but present the raw data in Appendix SIV.
Following Kerr et al. (2016), we visualized the 3-D position of all fish in each
flow and speed condition with heatmaps, to determine if fish were consistent in their
positions in HTF or LTF, perhaps to take advantage of regional flow conditions or “dead
spots”. To aid interpretation of the results, we plotted the standard deviation of position
per fish, flow condition and speed and fitted a rudimentary linear model per fish and flow
condition (Appendix SIV).
To determine the relationship between fish swimming kinematics, energetics, and
the ambient flow, the frequency components of the fish’s x-y-z position within the
respirometer were analysed. This analysis was undertaken to further ensure that any
periodic position fluctuations displayed by the fish were not a result of variables related
to the surrounding flow (i.e., condition or speed); that is, that periodic position
fluctuations were not indicative of fish using vortex structures to save energy. Periodicity
in the time series of (e.g., see Figure 3B, C, D, F, G, H) was detected for each
fish with Fisher’s g-statistic above 0.1 Hz due to the 3 fps sampling frequency (Wichert
et al., 2003). Space use analyses were completed in MATLAB (R2011a-R2014b;
Mathworks, Inc., Natick, MA, USA).
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Results
Swimming Energetics
The power functions describing the relationship between oxygen consumption rate (ṀO2)
and swimming speed (Figure 4) were:
Low-Turbulence Flow: (2)
High-Turbulence Flow:
(3)
Bacterial oxygen consumption rates ranged from 1.8-6.6 mg O2 h-1. The standard
deviation of the fish ID random effect, i.e., the intercept (equivalent to standard metabolic
rate), was 30.46 mg O2 kg-1 h-1.
At 0.5 BL s-1, fish in the HTF condition consumed 10.5 ( 6.4) mg O2 kg-1 h-1 (66%)
less than when in LTF (167.2 15.6) mg O2 kg-1 h-1). The exponent of the relationship was
significantly different between these flow conditions (t369 = -2.328, p = 0.0204);
differences between treatments occurred at speeds > 2 BL s-1. ṀO2 was not significantly
different between LTF and HTF speeds below 1.5 BL s-1 (paired t with FDR correction,
F7 < 1.889; p > 0.13; Figure 4). Fish consumed significantly less O2 in HTF vs. LTF
conditions at speeds above 2.0 BL s-1 (F7 > 3.038; p < 0.03; Figure 4). Beyond 2.0 BL s-1,
fish on average consumed 20% less oxygen in HTF vs. LTF conditions (range 0 – 46%;
Figure 4).
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Kinematics and Space Use
As expected (see e.g., Roche et al., 2014), predicted oxygen consumption
monotonically increased with pectoral fin beat frequency (Figure 5) in both flow
conditions. The factor-smooth interaction showed significant divergence between the two
flow conditions when the fin beat frequency was above 2.75 Hz, as evidenced in the
difference in 95% confidence intervals (±2 standard errors from the smooths of fin beat
frequency, Figure 5).
Overall space use in the tank can be visualized in heatmaps, following Kerr et al.
(2016), which do not suggest consistent positioning in the tank between fish and in
different flow and speed conditions (Figure 6). The centroid positions in x, y, and z
showed no consistent response to speed or flow condition (Appendix SIV). In both flow
conditions in the x- and y-directions, deviation decreased with increasing speed. In the x-
and y- directions, deviation was greater in HTF compared to LTF. For the z-direction,
there was little difference in deviation between LTF and HTF conditions. Further, there
was little effect of speed on deviation in HTF but a stronger effect of speed on deviation
in LTF (Appendix SIV). In combination with heatmaps (Figure 6), this approach
describes some idea of the behaviour of the fish in the tank. Overall, space use in LTF
was constrained to a small area at the front of the working section. In HTF, fish position
was diffused across a larger area (Figure 6).
Significant periodicity was detected in time series of (1.81±2.95 Hz;
mean±SD), (1.57±0.76 Hz) and (11.35±0.66 Hz), but in only a proportion of all
cases: x = 26/48; y = 34/48, z = 32/48.
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Discussion
Most studies of fish swimming and respirometry have used flow-straightening
devices that result in low-turbulence flow conditions within the experimental setup,
similar to the LTF condition described in this study. The natural habitat of most fishes is
more turbulent than that created by such laboratory conditions, but most studies seeking
to create more natural flows have focused on fish behaviour in coherent vortex structures,
which represent only a small portion of the flows encountered in their natural habitats
(Lacey et al., 2012; Kerr et al., 2016). In predictable vortex-dominated flows, it is
common for fish to display energy-saving behaviour (e.g., Kármán-gaiting) due to the
consistent nature of the periodic vortices (Liao, 2003; Liao et al., 2003). Few studies have
explicitly tested the effect of aperiodic, more randomized flow on fish swimming
energetics and kinematics. Of these, many have suggested that fish should expend more
energy in unsteady flows (Enders et al., 2003; Lupandin, 2005; Tritico and Cotel, 2010)
or show greater variation among individuals (Kerr et al., 2016), as each fish must
accommodate the unique flow structures it encounters. In the experiments described
herein, we compared oxygen consumption and swimming movements of fish in a low-
turbulence flow (LTF; similar to a standard fish respirometry study) versus a higher-
turbulence flow (HTF; mimicking a more natural turbulent environment). Fish displayed
significantly reduced metabolic costs when swimming in HTF compared to LTF. No
periodic components of the flow or swimming kinematics can account explicitly for these
energy savings, suggesting that fish may also be able to exploit turbulent flows without
discernible periodic wake formations.
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Fish have been shown to reduce the energetic costs of swimming (or otherwise
adapt to changes in ambient flow) in specific circumstances by employing behaviours
such as (1) gait switching (Korsmeyer et al., 2002), (2) Kármán-gaiting (Liao, 2003) , (3)
entraining (Webb, 1998), (4) bow riding (Newman and Wu, 1975; Taguchi and Liao,
2011), (5) tail holding (Kerr et al., 2016) and (6) wall holding (Kerr et al., 2016). Below,
the present results are discussed in the context of expected fish behaviour under these
different energy-reducing strategies to identify potential mechanisms behind the reduced
metabolic costs measured in this study.
We found that oxygen consumption increased significantly more with pectoral fin
use in LTF than in HTF, and caudal fin use was often absent in these MPF swimmers. At
high speeds prior to exhaustion, many MPF swimmers such as C. aggregata and other
labriform swimmers start complementing pectoral fin swimming with the caudal fin (i.e.,
at gait transition; Webb, 1973; Svendsen et al., 2010). Webb (1973) describes little-to-no
caudal fin use in C. aggregata at speeds below 3.4 BL s-1. Typically, at speeds 3.5-3.85
BL s-1, C. aggregata used occasional low-frequency, low-amplitude caudal fin beats
(caudal fin pattern A, Webb, 1973). Above 3.85 BL s-1, C. aggregata used 1-3 caudal fin
beats in quick succession to maintain position in the swimming flume (burst-coast
swimming; caudal fin pattern B, Webb, 1973), but this occurred over a short period of
time, immediately prior to exhaustion. Therefore, the overall proportion of time the
caudal fin is used even after initial recruitment of the caudal fin can remain low (Webb
1973, This study); gait transition in other labriforms has been shown to involve initial
occasional recruitment of the caudal fin before slowly developing to full and continuous
burst-coast (Cannas et al., 2006). In addition, the fish in our study were smaller (12.1 cm)
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than those used by Webb (1973; 14.3 cm), and therefore they are expected to start using
the tail at a higher relative speed (in BL s-1; Mussi et al., 2002) than that found by Webb
(1973). Further experiments focusing on fin and muscle use (pectoral fins vs. caudal fin
and red versus white muscle; e.g., Gerry and Ellerby, 2014), in unpredictable flow
regimes would better resolve the strength of the relationship between oxygen
consumption and movement patterns and the mechanism behind different movements in
complex flows.
Fish can reduce energetic expenditure by stationing behind a bluff body and alter
their body kinematics to synchronize with shed vortices. This behaviour, called Kármán-
gaiting (Liao, 2003), requires the presence of a bluff body which can shed vortices of a
size on the order of the fish’s body depth (Tritico and Cotel, 2010); no such bluff body
was available in the present experiments. The cross-tank body oscillation displayed by
fish in HTF (see e.g. Figure 3) is at first glance suggestive of such a behaviour; however,
this behaviour was not consistent between all fish, and the flow did not offer discrete
periodicity (Figure S3).
The orientation and/or size of vortices shed behind moving fins of MPF (median-
paired fin, sensu Webb 1984) swimmers differ from that of BCF (body-caudal-fin, sensu
Webb 1984) swimmers (Fish and Lauder (Drucker and Lauder, 1999; Drucker and
Lauder, 2002; Drucker et al., 2005; Fish and Lauder, 2006). Similarly, MPF swimmers
maintain a rigid body during locomotion at speeds below gait transition and are therefore
would not be able to use energy saving behaviour in the same manner as BCF swimmers,
i.e. by sychronising their tail beats with the vortex shedding frequency (Karman gaiting,
Liao, 2003). Little is known about how MPF swimmers may interact with vortices and
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turbulence in order to save energy. Interestingly, previous work has shown that, like BCF
swimmers (Marras et al 2015), MPF swimmers can save energy when swimming in the
wake of neighbors in a school (Johansen et al 2010). It is therefore possible that MPF
swimmers exploit paired fin motion kinematics and timing, in order to minimize the
energy spent for swimming in a turbulent flow. Simultaneous kinematic measurements
and PIV may better resolve the fine-scale movement responses of fish to moving flow
structures.
Further energy-saving mechanisms often involve station-holding either in front
(i.e. bow riding; Taguchi and Liao, 2011) or behind (i.e. entrainment; Liao, 2006;
Przybilla et al., 2010) bluff bodies where fish use resulting high pressure zones or lift and
wake suction forces, respectively, to maintain position. Fish have also been shown to
“tail-hold” by resting their tails against screens at the rear of experimental setups (Kerr et
al., 2016). These behaviours cannot explain the reduced energy consumption observed in
this study as there were no bluff bodies to station in front of, and fish generally stayed at
the front of the respirometer, with their tails 5-15 cm from the rear grid (see Figure 5).
Fish can also display “wall-holding” by potentially taking advantage of more stable and
reduced flows in the wall boundary layer (Kerr et al., 2016). While overall space use
(Figure 6) shows that fish in this experiment had a slight preference for swimming on the
left side of the respirometer, this positioning was dynamic in time. Fish moved back and
forth across the respirometer at higher flow velocities and in HTF (Figure 3). Any spatial
bias was therefore not likely to be due to standing flow features; that is, based on this
movement pattern and PIV there is no evidence of “dead zones” of low flow where fish
could consistently position themselves. In HTF, fish exhibited more movement across
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and along the test section (Figure 6). A comparison of the movements of one fish (Figure
3) and the heatmap of all fish (Figure 6) shows individuals differ in their absolute
position but that their positioning is consistently more variable in HTF. This could
indicate a passive behaviour, i.e. fish are being advected back and forth by the larger
turbulent eddies found in HTF, or an active behaviour, i.e. fish are exploiting temporary
(not periodic) vorticity that is higher in HTF than LTF to their advantage, in line with the
lower MO2 in HTF vs LTF conditions.
The results presented herein are not explained by previously-described energy-
saving mechanisms observed in fish. The fact that fish consume less oxygen when in
more turbulent conditions may be achieved through a higher variability in their positions
(compared to LTF), which in turn may help the fish to take advantage of the variability in
turbulent energy though time and space observed in HTF. However, the mechanism by
which this advantage is gained is not clear. The difference in energy consumption may
also be due to the interplay between skin friction drag and pressure drag on a given fish.
The Reynolds number of each fish ranged from approximately 5·105 to 5·106. This range
is close to the “drag crisis” regime, which is well-studied in spheres and cylinders (Smith
et al., 1999; Singh and Mittal, 2005; Kundu et al., 2011). In this regime, the boundary
layer over the surface of a bluff body transitions from a laminar to a fully turbulent state,
resulting in a smaller wake and lower pressure drag. In this case, the velocity
fluctuations in HTF may “trip” the boundary layer into the turbulent state, lowering the
pressure drag compared to LTF. Further investigation of this possibility would require
simultaneous PIV of the fish and flow.
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The PIV analysis described here characterises the flow and its eddies with no fish
in the tank; the same analysis with the fish swimming simultaneously in the flume (e.g.,
Drucker and Lauder, 2002) was not possible due to 1) potential alteration of fish
behaviour due to laser light, 2) optical inaccessibility due to the presence of the animal
and 3) animal welfare concerns over particulate density and non-infrared laser light. We
were therefore unable to examine the specific flow structure for each individual and
instead measured a “representative” flow field in each condition (throughout the range of
tested speeds) to be used for inference of all trials. Because of this, we cannot exclude the
possibility that the presence of the fish created unique flow features, such as persistent
zones of lower-than-average flow. However, if this were true we would expect to see
less-variable positioning in HTF as fish held station in these “self-generated dead zones”
to save energy. In fact, we see the opposite—less-variable position (and higher energy
consumption) in LTF. Further understanding of the mechanism behind the observed
behaviour could be achieved by conducting a similar experiment in which the fish
kinematics, the flow field surrounding the fish, and the fish’s ṀO2 are measured
simultaneously.
Both turbulence and coherent vortex structures can have passive and active effects
on fish, playing a role in postural control (Pavlov et al., 2000; Tritico and Cotel, 2010),
foraging (MacKenzie and Kiorboe, 1995), transportation costs (Webb and Cotel, 2010;
Webb et al., 2010), and orientation and swimming speed (Standen et al., 2004; Lupandin,
2005). It is critical that studies continue current research trends to determine the
energetic, kinematic, and behavioural effects of swimming in non-uniform, aperiodic
flows that mimic the diversity of turbulence observed in habitats. In particular, this study
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has shown that fish show significantly different patterns of positioning, kinematics and
energetics in a typical laboratory flume (LTF) vs. a more turbulent flow (HTF), at the
highest flow velocities. Individual and context-specific responses to variable flows in
terms of propulsive (Liao, 2003; Liao, 2004; Liao, 2007) or positioning strategies
(herein) must be understood to better interpret laboratory-based findings to natural
environments (Roche et al., 2014). Whether the effects of turbulence on energy
consumption are positive, neutral or negative (Enders et al., 2003), their quantification is
essential in understanding the energetics of swimming in semi-natural, varying flow
conditions (Cotel and Webb, 2015).
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Acknowledgements
We would like to thank Friday Harbor Laboratories for their facilities, space, and support
for this project, Mega Speed for the loan of the high-speed camera, and E.A. Variano
(UC Berkeley) for the loan of PIV laser equipment.
Funding
JVDH and MLB were supported by Stephen and Ruth Wainwright Fellowships. KO was
supported by the Natural Environmental Research Council, Fisheries Society of the
British Isles travel grant, and Kevin Schofield through Friday Harbor Laboratories’
Adopt-a-Student Program.
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obtained by radiotelemetry. Journal of Fish Biology 20, 479-489.
Webb, P. W. (1973). Kinematics of Pectoral Fin Propulsion in Cymatogaster Aggregata.
Journal of Experimental Biology 59, 697-710.
Webb, P. W. (1975). Hydrodynamics and energetics of fish propulsion. Bulletin of the
Fisheries Research Board of Canada 190, 1-158.
Webb, P. W. (1991). Composition and mechanics of routine swimming of rainbow trout,
Oncorhynchus mykiss. Canadian Journal of Fisheries and Aquatic Sciences 48, 583-590.
Webb, P. W. (1998). Entrainment by river chub Nocomis micropogon and smallmouth
bass Micropterus dolomieu on cylinders. Journal of Experimental Biology 201, 2403-
2412.
Webb, P. W. and Cotel, A. J. (2010). Turbulence: does vorticity affect the structure and
shape of body and fin propulsors? Integrative and comparative biology 50, 1155-66.
Webb, P. W., Cotel, A. J. and Meadows, L. A. (2010). Waves and eddies: effects on
fish behavior and habitat distribution. In Fish locomotion: an eco-ethological perspective,
eds. P. Domenici and B. G. Kapoor). Boca Raton, FL: CRC Press.
Wichert, S., Fokianos, K. and Strimmer, K. (2003). Identifying periodically expressed
transcripts in microarray time series data. Bioinformatics 20, 5-20.
Wood, S. (2017). Generalized Additive Models: An Introduction with R Chapman and
Hall/CRC.
Zuur, A. F., Ieno, E. N. and Elphick, C. S. (2010). A protocol for data exploration to
avoid common statistical problems. Methods in Ecology and Evolution 1, 3-14.
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Figures
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Figure 1. Experimental setup. A) Diagram of top and side views of the experimental
setup, shown in the low-turbulence flow condition with flow straightener present. The
laser plane (top view, dot-dashed line) was used for Particle Image Velocimetry (PIV)
measurement. The flow straightener was not included in the high turbulence flow (HTF)
condition. B) Flow straightener and fine-mesh grid used for filtering out large eddies
from the LTF condition. C) Large-opening grid used to restrain fish in the HTF condition,
with no flow straightener.
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Figure 2. Sample vector fields of the lateral view of the test section from the (A) low-
(LTF) and (B) high-turbulence flow (HTF) conditions, at the same mean streamwise
velocity (0.38 m s-1). Mean streamwise velocity has been subtracted to reveal coherent
structures; colormap shows vorticity (s-1). Direction of flow is from left to right, with
swimming chamber walls on the top and bottom and the two different grids on the left,
qualitatively represented by black dashed lines.
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Figure 3. 3D position of one fish in a swimming respirometer in low- (LTF; red) and
high-turbulence flow (HTF; blue) conditions. All snout positions ((𝑥𝑠, 𝑦𝑠, 𝑧𝑠); coloured
symbols), centroid positions ((𝑥𝑐, 𝑦𝑐, 𝑧𝑐 ); black symbols) and standard deviation (black
lines) of one sample fish swimming in LTF (red) and HTF (blue) at 1.5 BL s-1 (A, B, C,
D) and 4.0 BL s-1 (E, F, G, H), along with time series of 𝑥𝑠, 𝑦𝑠 and 𝑧𝑠 (B, C, D, F, G, H).
The x=0 position represents the location of the grid in both LTF and HTF. Thicker lines
represent the location of the tank walls, and arrows indicate flow direction (see also
Figure 1).
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Figure 4. Mean oxygen consumption rate (ṀO2; mg O2 kg-1 h-1) is significantly
higher in LTF (red) than in HTF (blue) at swimming speeds > 2 BL s-1. Symbols
represent ṀO2 measurements for each fish (n = 8) at each speed and condition. Solid
lines represent fitted curves.
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Figure 5. Oxygen consumption (ṀO2; mg O2 kg-1 h-1) increases with pectoral fin
beat frequency (Hz) in low-turbulence (LTF; red letters) and in high-turbulence
flow (HTF; blue letters). Predicted oxygen consumption as a function of pectoral fin
beat frequency in n = 8 shiner perch (solid lines), along with 95% confidence intervals
(dashed lines). Data are shown as letters indicating the flow speed (L = Low, 0.5 BL s-1;
M = Medium, 1.5 BL s-1; H = High, shared Umax, 3.5-4.5 BL s-1. The observed value of
fish ID is conditioned on in the predictions. Confidence bands are wider at either end of
the plot range as there is no data beyond the range and there is greater uncertainty about
the shape of the smooth when there is no previous/further data.
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Figure 6. Overall heatmap of space use in x, y and z dimensions of all n = 8 shiner perch
in a swimming respirometer in low- (LTF; left) and high- (HTF; right) turbulence flow
conditions, at low, medium and high flow speeds. Arrows indicate flow direction,
including flow into the page (circle with x).
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Table 1. Turbulence parameters from this study (both low-turbulence flow (LTF)
and high-turbulence flow (HTF)) as compared to field-measured quantities from the
coastal habitats of e.g., shiner perch, C. aggregata.
Property Current
study
(LTF)
Current
study
(HTF)
Natural habitat
[s-1] 2 - 23 4 - 62 4 – 6400 (surf zone)
0 – 25 (inlets and estuaries)
(Fuchs and Gerbi, 2016)
[m2 s-3] 10-4.5 – 10-3.5 10-4.2 – 10-2.8 10-3.5-100 (intertidal)
(Gaylord et al., 2013)
10-7.2 – 10-3 (coastal bay with
waves)
(Jones and Monismith, 2008)
𝑇𝐾𝐸 10-4.7 – 10-3.7 10-4.1 – 10-2.9 10-4 – 100 (tidal channel)
(Guerra and Thomson, 2017)
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AppendixSIVJulie van der Hoop
26 Feb 2018
This R Markdown document details the statistical approach for the paper van der Hoop et al. 201X “Turbulentflow reduces oxygen consumption in the labriform swimming shiner perch, Cymatogaster aggregata”
The data represent mean oxygen consumption rates (MO2; mg O_2/kg/h) from three measurements at eachspeed (repetition number) of increments from 0.5 Body Lengths (BL) per second [BL/s] up to a maximumswimming speed, for different Fish that swam each in High (“T”) and Low (“L”) turbulence flow conditionsin a respirometer. Bacterial MO2 (mg O_2/h) for each trial are subtracted from the measured MO2.## 1. Data handling
# load datalibrary(readxl)fish <- read_xlsx("FHL_FishVO2_allreps.xlsx")
# make the things that need to be factors factorsfish$Fish <- as.factor(fish$Fish)fish$Flow <- as.factor(fish$Flow)fish$Rep <- as.factor(fish$Rep)
## 2. Model Fittinglibrary(nlme)
# We want to fit something of the form# O2 ~ a + b*Speed^c# estimate a,b,c and have a random effect for fish# each a,b,c has two levels, one for each treatment (Low-Turbulence and High-Turbulence)
# NOTES:# - formula is NOT a standard R formula# - fixed specifies the form for the fixed effects (the a,b,c parameters)# - random says what the random effects are (random intercept for a)modr <- nlme(VO2minBac~a+b*Speed^c,
fixed = a+b+c~Flow,random = a+b+c~1|Fish,start=c(168.7038472,0, 6,0, 2.2036793, 0),data=fish)
# Check model summarysummary(modr)
## Nonlinear mixed-effects model fit by maximum likelihood## Model: VO2minBac ~ a + b * Speed^c## Data: fish## AIC BIC logLik## 3866.919 3918.209 -1920.459#### Random effects:## Formula: list(a ~ 1, b ~ 1, c ~ 1)
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## Level: Fish## Structure: General positive-definite, Log-Cholesky parametrization## StdDev Corr## a.(Intercept) 1.910258e+01 a.(In) b.(In)## b.(Intercept) 7.802433e-08 -0.138## c.(Intercept) 3.073572e-01 0.210 -0.658## Residual 3.442769e+01#### Fixed effects: a + b + c ~ Flow## Value Std.Error DF t-value p-value## a.(Intercept) 167.19921 8.246068 369 20.276233 0.0000## a.FlowT -10.53301 6.418565 369 -1.641023 0.1016## b.(Intercept) 4.99231 1.157339 369 4.313611 0.0000## b.FlowT 1.42991 2.435864 369 0.587026 0.5575## c.(Intercept) 2.89096 0.196620 369 14.703291 0.0000## c.FlowT -0.66851 0.287043 369 -2.328942 0.0204## Correlation:## a.(In) a.FlwT b.(In) b.FlwT c.(In)## a.FlowT -0.340## b.(Intercept) -0.411 0.370## b.FlowT 0.108 -0.672 -0.270## c.(Intercept) 0.413 -0.275 -0.825 0.220## c.FlowT -0.142 0.623 0.388 -0.981 -0.324#### Standardized Within-Group Residuals:## Min Q1 Med Q3 Max## -2.4264658 -0.5157803 -0.1067824 0.4336127 5.5249318#### Number of Observations: 382## Number of Groups: 8# plot observed vs predictedplot(fish$VO2minBac, predict(modr),
asp=1,xlab="Observed VO2minBac", ylab="Predicted VO2minBac")
abline(a=0,b=1, col="blue", lty=2)
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Observed VO2minBac
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# same but average over repetitions# (a bit cleaner)plot(aggregate(fish$VO2minBac, list(fish$Speed, fish$Flow, fish$Fish), mean)$x,
aggregate(predict(modr), list(fish$Speed, fish$Flow, fish$Fish), mean)$x,main="modr - aggregated observed vs predicted",asp=1,xlab="Observed VO2minBac", ylab="Predicted VO2minBac")
abline(a=0,b=1, col="blue", lty=2)
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modr − aggregated observed vs predicted
Observed VO2minBac
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## 3. Model checking
# per fish residuals - this looks okay, no major variationsbp_dat <- data.frame(resids = residuals(modr),
Fish = fish$Fish)boxplot(resids~Fish, bp_dat, varwidth=TRUE, ylim=c(-100, 200))
5 6 9 10 11 13 15 19
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# residuals by Speed# - these look okay too, maybe some increase in variance at higher speedsdat <- data.frame(residuals = residuals(modr),# Speed = cut(fish$Speed, seq(0.25,4.75,0.5)))
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Speed = cut(fish$Speed, c(seq(0.25,3.75,0.5), 4.75)))boxplot(residuals~Speed, dat, varwidth=TRUE, ylim=c(-100, 200))
(0.25,0.75] (1.25,1.75] (2.25,2.75] (3.25,3.75]
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# predictions vs. residualsplot(modr)
Fitted values
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plot(modr, resid(.) ~ Speed)
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# what aout a q-q plot of the residuals# - not perfect: looks like we aren't doing such a good job in the tails?qqnorm(modr, abline=c(0,1))
Standardized residuals
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# q-q of the random effects - they should be normalqqnorm(modr, ~ranef(.))
Random effects
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a.(Intercept)
−1.0e−07 0.0e+00
b.(Intercept)
−0.4 −0.2 0.0 0.2 0.4 0.6
c.(Intercept)
## 4. prediction plotslibrary(ggplot2)
# plot predictions per Fish# make prediction grid, then predictpreddat <- expand.grid(Speed = seq(0.5, 4.5, by=0.1),
Flow = c("L", "T"), # L = LTF, T = HTFFish = unique(fish$Fish))
plotty <- predict(modr, preddat, level=1)plotty <- cbind(preddat, VO2minBac=plotty)
p <- ggplot(plotty, aes(x=Speed, y=VO2minBac, group=Flow, colour=Flow)) +geom_line(size=0.75, linetype=2) +geom_point(data=fish) +facet_wrap(~Fish, nrow=2) +theme_minimal() +# scale_colour_brewer(type="qual")scale_color_manual(values=c('blue', 'red')) +scale_shape_manual(values=c(17, 16))+labs(x="Speed (BL/s)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition")
print(p)
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# plot predictions averaged over Fish# make prediction grid, then predictpreddat <- expand.grid(Speed = seq(0.5, 4.5, by=0.1),
Flow = c("L", "T"))plotty <- predict(modr, preddat, level=0)plotty <- cbind(preddat, VO2minBac=plotty)
p <- ggplot(plotty, aes(x=Speed, y=VO2minBac, group=Flow, colour=Flow)) +geom_line(size=0.75, linetype=2) +geom_point(data=fish, size=1.5, aes(shape=Flow)) +theme_minimal() +scale_colour_manual(values=c("red", "blue")) +scale_shape_manual(values=c(17, 16))+labs(x="Speed (BL/s)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition")
print(p)
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# Paired data for comparison of MO2 between LTF and HTF at each speedpaireddata <- read_xlsx("/Users/julievanderhoop/Documents/Courses/Biol533_FishSwimming_FHL/VO2.xlsx", sheet = 11) # read 11th sheet
t05 <- t.test(paireddata$L[which(paireddata$Speed==0.5)],paireddata$T[which(paireddata$Speed==0.5)],paired = TRUE)t1 <- t.test(paireddata$L[which(paireddata$Speed==1)],paireddata$T[which(paireddata$Speed==1)],paired = TRUE)t15 <- t.test(paireddata$L[which(paireddata$Speed==1.5)],paireddata$T[which(paireddata$Speed==1.5)],paired = TRUE)t2 <- t.test(paireddata$L[which(paireddata$Speed==2.0)],paireddata$T[which(paireddata$Speed==2.0)],paired = TRUE)t25 <- t.test(paireddata$L[which(paireddata$Speed==2.5)],paireddata$T[which(paireddata$Speed==2.5)],paired = TRUE)t3 <- t.test(paireddata$L[which(paireddata$Speed==3.0)],paireddata$T[which(paireddata$Speed==3.0)],paired = TRUE)t35 <- t.test(paireddata$L[which(paireddata$Speed==3.5)],paireddata$T[which(paireddata$Speed==3.5)],paired = TRUE)t4 <- t.test(paireddata$L[which(paireddata$Speed==4.0)],paireddata$T[which(paireddata$Speed==4.0)],paired = TRUE)
pvals <- c(t05$p.value,t1$p.value,t15$p.value,t2$p.value,t25$p.value,t3$p.value,t35$p.value,t4$p.value)BH <- p.adjust(pvals,"BH")
To assess how MO2 changed with fin beat frequency, we fitted a generalized additive model (Wood, 2017) tothe MO2, using pectoral or caudal fin beat (Hz) as separate explanatory variables. We used factor-smoothinteractions (Baayen et al., 2016) to fit two levels of a smoothed function of measured beat frequency, onefor each flow condition. Such terms fit the base level of the factor as a smooth, then model deviations fromthat smooth for the other level, thus information is shared between the models while allowing for a flexiblerelationship that makes no assumptions about functional form. Fish ID was included as a random effect.Models were fitted by restricted maximum likelihood.hz <- read.csv("/Users/julievanderhoop/Documents/Courses/Biol533_FishSwimming_FHL/FishVO2Hz.csv")
# make codes for the speedshz$speedcode <- "H"hz$speedcode[hz$speed == 0.5] <- "L"
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hz$speedcode[hz$speed == 1.5] <- "M"# speeds set at 0.5, 1.5 and then the max speed achieved for both LTF and HTF
library(ggplot2)
# quick visualisationp <- ggplot(hz) +
#geom_point(aes(x=speed, y=VO2minBac, colour=cond)) +geom_point(aes(x=PecHz, y=VO2minBac, colour=cond)) +theme_minimal() +scale_shape_manual(values=c(16, 17)) +scale_color_manual(values=c('red', 'blue')) +labs(x="Pectoral Fin Beat Frequency (Hz)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition")+facet_wrap(~Fish)
print(p)
F6 F9
F15 F19 F5
F10 F11 F13
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1 2 3
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# Fit a GAMlibrary(mgcv)
## Warning: package 'mgcv' was built under R version 3.4.2
## This is mgcv 1.8-22. For overview type 'help("mgcv-package")'.# this is fitting a model that says:# O2 varies as a function of pectoral hz, but we should estimate a different# curve for each condition. We also think that fish acts like a random effectb_pec <- gam(VO2minBac~s(PecHz, cond, bs="fs") + s(Fish, bs="re"),
data=hz, method="REML")
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# check this modelgam.check(b_pec)
−100 −50 0 50 100
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theoretical quantiles
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Resids vs. linear pred.
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Response vs. Fitted Values
Fitted Values
Res
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#### Method: REML Optimizer: outer newton## full convergence after 7 iterations.## Gradient range [-0.0001462202,0.0001143156]## (score 264.0581 & scale 2259.291).## Hessian positive definite, eigenvalue range [0.0001462017,24.05956].## Model rank = 29 / 29#### Basis dimension (k) checking results. Low p-value (k-index<1) may## indicate that k is too low, especially if edf is close to k'.#### k' edf k-index p-value## s(PecHz,cond) 20.00 6.49 0.97 0.38## s(Fish) 8.00 4.37 NA NA# Little heteroskedasticity (top right). Looks like the model predicts well (bottom# right). Residuals look normal enough (left side). Text output shows that we have# allowed for sufficient flexibility in our model.summary(b_pec)
#### Family: gaussian## Link function: identity#### Formula:## VO2minBac ~ s(PecHz, cond, bs = "fs") + s(Fish, bs = "re")
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#### Parametric coefficients:## Estimate Std. Error t value Pr(>|t|)## (Intercept) 222.69 63.07 3.531 0.00115 **## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#### Approximate significance of smooth terms:## edf Ref.df F p-value## s(PecHz,cond) 6.489 19 15.001 <2e-16 ***## s(Fish) 4.368 7 1.595 0.0251 *## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#### R-sq.(adj) = 0.852 Deviance explained = 88.6%## -REML = 264.06 Scale est. = 2259.3 n = 48# v. high % deviance explained, will continue to include the fish random effect# to explicitly include between-fish variability
# now to make predictions, make a grid of values with all the pectoral hz we need# plus values for the condition and fishpreddat <- expand.grid(PecHz = seq(0.5, 3.5, by=0.1),
cond = c("T", "L"),Fish = unique(hz$Fish))
# make predictions, also predict the standard errorpr <- predict(b_pec, preddat, type="response", se=TRUE)preddat$VO2minBac <- pr$fit# generate the CIspreddat$upper <- pr$fit + 2*pr$se.fitpreddat$lower <- pr$fit - 2*pr$se.fit
# what does that look like?p <- ggplot(hz) +
geom_line(aes(x=PecHz, y=VO2minBac, colour=cond, group=cond), data=preddat) +geom_line(aes(x=PecHz, y=upper, colour=cond, group=cond), linetype=2, data=preddat) +geom_line(aes(x=PecHz, y=lower, colour=cond, group=cond), linetype=2, data=preddat) +geom_text(aes(x=PecHz, y=VO2minBac, colour=cond, label=speedcode)) +# scale_colour_brewer(type="qual") +theme_minimal() +scale_color_manual(values=c('blue', 'red')) +labs(x="Pectoral Fin Beat Frequency (Hz)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition")+facet_wrap(~Fish, nrow=2)
print(p)
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L M
H
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F19 F5 F6 F9
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Pectoral Fin Beat Frequency (Hz)
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Condition
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# ignore fish and predict integrating out the fish random effectpreddat <- expand.grid(PecHz = seq(0.5, 3.5, by=0.1),
cond = c("T", "L"), Fish="F5")pr <- predict(b_pec, preddat, type="response", se=TRUE, exclude="s(Fish)")preddat$VO2minBac <- pr$fitpreddat$upper <- pr$fit + 2*pr$se.fitpreddat$lower <- pr$fit - 2*pr$se.fit
# what does that look like?p <- ggplot(hz) +
geom_line(aes(x=PecHz, y=VO2minBac, colour=cond, group=cond), data=preddat) +geom_line(aes(x=PecHz, y=upper, colour=cond, group=cond), linetype=2, data=preddat) +geom_line(aes(x=PecHz, y=lower, colour=cond, group=cond), linetype=2, data=preddat) +geom_text(aes(x=PecHz, y=VO2minBac, colour=cond, label=speedcode)) +# scale_colour_brewer(type="qual") +# scale_shape_manual(values=c(16, 17))+scale_color_manual(values=c('blue', 'red'))+theme_minimal() +labs(x="Pectoral Fin Beat Frequency (Hz)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition")
print(p)
Journal of Experimental Biology 221: doi:10.1242/jeb.168773: Supplementary information
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Pectoral Fin Beat Frequency (Hz)
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Condition
a
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Wewere interested in testing the relationship between oxygen consumption and caudal fin use or frequency;however, the caudal fin was rarely used and was 0 in 65% of the experimental conditions. Model formulationand figures of the raw data are included below to illustrate the limitations of the data and the observedcaudal fin use patterns.# quick visualisationp <- ggplot(hz) +
geom_point(aes(x=CaudHz, y=VO2minBac, colour=cond)) +theme_minimal() +scale_shape_manual(values=c(16, 17)) +scale_color_manual(values=c('red', 'blue')) +labs(x="Caudal Fin Beat Frequency (Hz)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition") +facet_wrap(~Fish)
print(p)
## Warning: Removed 1 rows containing missing values (geom_point).
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F6 F9
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F10 F11 F13
0 1 2 3 4 5 0 1 2 3 4 5
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Caudal Fin Beat Frequency (Hz)
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2 (m
g.kg
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Condition
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# try the same kind of model as above for the caudal fin frequency# need to reduce k (smooth complexity) as we don't have many unique valuesb_caud <- gam(VO2minBac~s(CaudHz, cond, bs="fs", k=5) + s(Fish, bs="re"),
data=hz, method="REML")
# model checksummary(b_caud)
#### Family: gaussian## Link function: identity#### Formula:## VO2minBac ~ s(CaudHz, cond, bs = "fs", k = 5) + s(Fish, bs = "re")#### Parametric coefficients:## Estimate Std. Error t value Pr(>|t|)## (Intercept) 458.9 105.8 4.338 8.7e-05 ***## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#### Approximate significance of smooth terms:## edf Ref.df F p-value## s(CaudHz,cond) 3.555e+00 8 2.311 0.00123 **## s(Fish) 7.269e-05 7 0.000 0.66065## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
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## R-sq.(adj) = 0.287 Deviance explained = 34.2%## -REML = 285.97 Scale est. = 10942 n = 47# less deviance explained than beforeplot(b_caud)
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s(C
audH
z,co
nd,3
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s(Fish,0)
Gaussian quantiles
effe
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# do we believe that O2 is n-shaped in caudal hz? Unlikely
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preddat <- expand.grid(CaudHz = seq(0, 5, by=0.1),cond = c("T", "L"),Fish = unique(hz$Fish))
preddat$VO2minBac <- predict(b_caud, preddat, type="response")
p <- ggplot(hz) +geom_line(aes(x=CaudHz, y=VO2minBac, colour=cond, group=cond), data=preddat) +geom_text(aes(x=CaudHz, y=VO2minBac, colour=cond, label=speedcode)) +# scale_colour_brewer(type="qual") +theme_minimal() +labs(x="Caudal Hz", colour="Condition") +scale_shape_manual(values=c(16, 17)) +scale_color_manual(values=c('red', 'blue')) +labs(x="Caudal Fin Beat Frequency (Hz)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition") +facet_wrap(~Fish, nrow=2)
print(p)
## Warning: Removed 1 rows containing missing values (geom_text).
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Caudal Fin Beat Frequency (Hz)
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## what about caudal use? Will have the same data limitation (when Hz = 0, use = 0)
# quick visualisationp <- ggplot(hz) +
geom_point(aes(x=Cauduse, y=VO2minBac, colour=cond)) +
Journal of Experimental Biology 221: doi:10.1242/jeb.168773: Supplementary information
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theme_minimal() +scale_shape_manual(values=c(16, 17)) +scale_color_manual(values=c('red', 'blue')) +labs(x="Caudal Fin Use (%)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition") +facet_wrap(~Fish)
print(p)
F6 F9
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Caudal Fin Use (%)
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T
# try the same kind of model as above for the caudal fin use# need to reduce k (smooth complexity) as we don't have many unique valuesb_caud <- gam(VO2minBac~s(Cauduse, cond, bs="fs", k=5) + s(Fish, bs="re"),
data=hz, method="REML")
# model checksummary(b_caud)
#### Family: gaussian## Link function: identity#### Formula:## VO2minBac ~ s(Cauduse, cond, bs = "fs", k = 5) + s(Fish, bs = "re")#### Parametric coefficients:## Estimate Std. Error t value Pr(>|t|)## (Intercept) 235.85 17.24 13.68 <2e-16 ***## ---
Journal of Experimental Biology 221: doi:10.1242/jeb.168773: Supplementary information
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## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#### Approximate significance of smooth terms:## edf Ref.df F p-value## s(Cauduse,cond) 2.288983 9 4.73 5.49e-08 ***## s(Fish) 0.001065 7 0.00 0.532## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#### R-sq.(adj) = 0.475 Deviance explained = 50.1%## -REML = 282.88 Scale est. = 8019.5 n = 48# less deviance explained than beforeplot(b_caud)
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010
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Cauduse
s(C
audu
se,c
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2.29
)
Journal of Experimental Biology 221: doi:10.1242/jeb.168773: Supplementary information
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−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
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# do we believe that O2 is n-shaped in caudal hz? Unlikely
preddat <- expand.grid(Cauduse = seq(0, 45, by=1),cond = c("T", "L"),Fish = unique(hz$Fish))
preddat$VO2minBac <- predict(b_caud, preddat, type="response")
p <- ggplot(hz) +geom_line(aes(x=Cauduse, y=VO2minBac, colour=cond, group=cond), data=preddat) +geom_text(aes(x=Cauduse, y=VO2minBac, colour=cond, label=speedcode)) +# scale_colour_brewer(type="qual") +theme_minimal() +labs(x="Caudal Hz", colour="Condition") +scale_shape_manual(values=c(16, 17)) +scale_color_manual(values=c('red', 'blue')) +labs(x="Caudal Fin Use (%)", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition") +facet_wrap(~Fish, nrow=2)
print(p)
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Caudal Fin Use (%)
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## and CV of pectoral fin beat frequency (following Roche et al. 2014)# quick visualisationp <- ggplot(hz) +
geom_point(aes(x=CV.Pec, y=VO2minBac, colour=cond)) +theme_minimal() +scale_shape_manual(values=c(16, 17)) +scale_color_manual(values=c('red', 'blue')) +labs(x="CV of Pectoral Fin Beat Frequency", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition") +facet_wrap(~Fish)
print(p)
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F6 F9
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CV of Pectoral Fin Beat Frequency
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# try the same kind of model as above for the caudal fin use# need to reduce k (smooth complexity) as we don't have many unique valuesb_cvpec <- gam(VO2minBac~s(CV.Pec, cond, bs="fs", k=5) + s(Fish, bs="re"),
data=hz, method="REML")
# model checksummary(b_cvpec)
#### Family: gaussian## Link function: identity#### Formula:## VO2minBac ~ s(CV.Pec, cond, bs = "fs", k = 5) + s(Fish, bs = "re")#### Parametric coefficients:## Estimate Std. Error t value Pr(>|t|)## (Intercept) 180.79 95.78 1.888 0.066 .## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#### Approximate significance of smooth terms:## edf Ref.df F p-value## s(CV.Pec,cond) 4.8544608 9 3.29 0.000121 ***## s(Fish) 0.0004511 7 0.00 0.947203## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
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## R-sq.(adj) = 0.387 Deviance explained = 45%## -REML = 290.95 Scale est. = 9375.6 n = 48# less deviance explained than beforeplot(b_cvpec)
0.1 0.2 0.3 0.4 0.5 0.6 0.7
020
040
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CV.Pec
s(C
V.P
ec,c
ond,
4.85
)
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001
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Gaussian quantiles
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# do we believe that O2 is n-shaped in caudal hz? Unlikely
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preddat <- expand.grid(CV.Pec = seq(0, 0.75, by=0.1),cond = c("T", "L"),Fish = unique(hz$Fish))
preddat$VO2minBac <- predict(b_cvpec, preddat, type="response")
p <- ggplot(hz) +geom_line(aes(x=CV.Pec, y=VO2minBac, colour=cond, group=cond), data=preddat) +geom_text(aes(x=CV.Pec, y=VO2minBac, colour=cond, label=speedcode)) +# scale_colour_brewer(type="qual") +theme_minimal() +# scale_shape_manual(values=c(16, 17)) +scale_color_manual(values=c('blue', 'red')) +labs(x="CV of Pectoral Fin Beat Frequency", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition") +facet_wrap(~Fish, nrow=2)
print(p)
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CV of Pectoral Fin Beat Frequency
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a
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L
# plot all together by integrating out fish random effectpreddat <- expand.grid(CV.Pec = seq(0, 0.75, by=0.1),
cond = c("T", "L"), Fish="F5")pr <- predict(b_cvpec, preddat, type="response", se=TRUE, exclude="s(Fish)")preddat$VO2minBac <- pr$fitpreddat$upper <- pr$fit + 2*pr$se.fitpreddat$lower <- pr$fit - 2*pr$se.fit
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# what does that look like?p <- ggplot(hz) +
geom_line(aes(x=CV.Pec, y=VO2minBac, colour=cond, group=cond), data=preddat) +geom_line(aes(x=CV.Pec, y=upper, colour=cond, group=cond), linetype=2, data=preddat) +geom_line(aes(x=CV.Pec, y=lower, colour=cond, group=cond), linetype=2, data=preddat) +geom_text(aes(x=CV.Pec, y=VO2minBac, colour=cond, label=speedcode)) +# scale_colour_brewer(type="qual") +# scale_shape_manual(values=c(16, 17))+scale_color_manual(values=c('blue', 'red'))+theme_minimal() +labs(x="CV of Pectoral Fin Beat Frequency", y = expression("Oxygen Consumption Rate, MO"[2]* " ("*mg.kg^{-1}*.h^{-1}*")"), colour="Condition")
print(p)
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CV of Pectoral Fin Beat Frequency
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To investigate the position of fish in the tank, we compared the centroid locations of the snout of each fishthrough the 180s sample period, and standard deviation from that centroid position, in different speed*flowcombinations. This investigation along with the heatmaps (Figure 5) illustrate the overall positioning ofindividuals within the tank; however our interpretation is limited due to the number of response parameterscompared to the number of animals tested and the factors to be considered.
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